Star formation efficiency and scaling relations in parsec-scale cluster-forming clumps

Numerical simulations predict that clumps (⁠∼1 pc) should form stars at high efficiency to produce bound star clusters. We conducted a statistical study of 17 nearby cluster-forming clumps to examine the star formation rate and gas mass surface density relations (i.e. ΣSFR versus Σgas⁠) at the clump scale. Using near-infrared point sources and Herschel dust continuum analysis, we obtained the radius, age, and stellar mass for most clusters in the ranges 0.5-1.6 pc, 0.5-1.5 Myr, 40-500 M⊙⁠, respectively, and also found that they are associated with Σgas values ranging from 80 to 600 M⊙ pc−²⁠. We obtained the best-fitting scaling relations as ΣSFR ∝ Σgas1.46 and ΣSFR ∝ (Σgas/tff)^0.80 for the studied sample of clumps. Comparing our results with existing scaling relations at cloud and extragalactic scales, we found that while the power-law exponent obtained in this work is similar to those found at these scales, the star formation rate surface densities are relatively higher for similar gas mass surface densities. From this work, we obtained instantaneous median star formation efficiency (SFE) and efficiency per free-fall time (⁠ϵff⁠) of ∼20 per cent and ∼13 per cent, respectively, for the studied clumps. We discuss the cause of the obtained high SFE and ϵff in the studied clumps and also discuss the results in the context of bound cluster formation within molecular clouds. We conclude that our results do not favour a universal scaling law with a constant value of ϵff in star-forming systems across different scales.